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A note on the cyclotomic polynomial

Published online by Cambridge University Press:  26 February 2010

I. J. Schoenberg
I. J. Schoenberg
Affiliation:
University of Pennsylvania and Institute for Advanced Study.
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Extract

The n-th roots of unity 1, ω, …, ωn-1, where ω = exp (2πi\n), are linearly dependent in the field Q of rationals since, for instance, their sum vanishes. We are here concerned with the linear relations between them with integral coefficients. Let U denote the vector space of elements u = (u0, …, un−1) over Q and let N be the subspace of elements u defined by the relation u0+u1ω+…+un−1ωn−1=0. (1)

Type
Research Article
Information
Mathematika , Volume 11 , Issue 2 , December 1964 , pp. 131 - 136
Copyright
Copyright © University College London 1964

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References

1. Smith, H. J. S., “On systems of linear indeterminate equations and congruences”, No. XII in Collected mathematical papers, vol. 1, (Oxford, 1894).Google Scholar
2. Tschebotaröw, N. and Schwerdtfeger, H., Grundzüge der Galoisschen Theorie, (Groningen, 1950).Google Scholar